Functions in R are objects that carry out operations on *arguments* that are supplied to them and return one or more values. The syntax for writing a function is

function (argument list) body

The first component of the function declaration is the keyword function, which indicates to R that you want to create a function. An argument list is a comma-separated list of formal arguments. A formal argument can be a symbol (i.e. a variable name such as *x* or *y*), a statement of the form symbol = expression (e.g. pch=16) or the special formal argument ... (triple dot). The body can be any valid R expression or set of R expressions. Generally, the body is a group of expressions contained in curly brackets { }, with each expression on a separate line. Functions are typically assigned to symbols, but they need not to be. This will only begin to mean anything after you have seen several examples in operation.

The mean is the sum of the numbers Σ*y* divided by the number of numbers *n* = Σ 1 (summing over the number of numbers in the vector called *y*). The R function for *n* is length(y) and for Σ*y* is sum(y), so a function to compute arithmetic means is

`arithmetic.mean<-function(x) sum(x)/length(x)`

We should test the function with some data where we know the right answer:

y<-c(3,3,4,5,5) arithmetic.mean(y) [1] 4

Needless to say, there is a built-in function for arithmetic means called mean:

```
mean(y)
[1] 4
```

The median ...

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